I'm here to help you. I'm sorry if you were expecting something other than a thorough revision of the issue, so please don't worry about paying me for my time.
Back to the issue, inlet heater hose should be hotter than outlet having gone through the heater core. If both hoses are at the same temperature, then check for a possible air bubble left in the system impeding circulation after flushing the heater core. If that's the case, here is the procedure for filling the system up:
REFILLING COOLING SYSTEM
- Tighten the radiator draincock and the cylinder block drain plug(s) (if removed).
CAUTION: Failure to purge air from the cooling system can result in an overheating condition and severe engine damage.
- Fill system using a 50/50 mixture of ethylene glycol antifreeze and low mineral content water. Fill pressure bottle to service line and install cap.
NOTE: The engine cooling system will push any remaining air into the coolant bottle within about an hour of normal driving. As a result, a drop in coolant level in the pressure bottle may occur. If the engine cooling system overheats and pushes coolant into the overflow side of the coolant bottle, this coolant will be sucked back into the cooling system ONLY IF THE PRESSURE CAP IS LEFT ON THE BOTTLE. Removing the pressure cap breaks the vacuum path between the two bottle sections and the coolant will not return to cooling system.
- With heater control unit in the HEAT position, operate engine with pressure bottle cap in place.
- Add coolant to pressure bottle as necessary. Only add coolant to the pressure bottle when the engine is cold. Coolant level in a warm engine will be higher due to thermal expansion.
NOTE: The coolant bottle has two chambers. Coolant will normally only be in the outboard (larger) of the two. The inboard chamber is only to recover coolant in the event of an overheat or after a recent service fill. The inboard chamber should normally be empty. If there is coolant in the overflow side of the coolant bottle (after several warm/cold cycles of the engine) and coolant level is above cold full when cold, disconnect the end of the overflow hose at the fill neck and lower it into a clean container. Allow coolant to drain into the container until emptied. Reconnect overflow hose to fill neck.
Another possibility could be a combustion chamber leak from a bad head gasket allowing gases into the cooling system. To test that possibility, you could borrow a block tester kit from any of the major auto parts retailers.
Once again, my goal is to help you solve your issue, everything else is secondary.